5 a day: five daily revision questions for Year 11 pupils


Head of mathematics and co-creator of Imvoto

Today we are excited to explain about our “5 a day” revision questions aimed at Year 11 pupils who are about to take their GCSE Mathematics exams. Each set of five questions is designed to be quite short: we want to encourage pupils to do some maths every day in the run up to the summer examinations. Each day we cover a variety of mixed topics, ensuring that pupils (and their teachers) gain an awareness of what they can and cannot do across the range of assessed content.

We will be publishing two levels of questions each day: one aimed at pupils who will take higher tier, the other at foundation tier. After pupils have sat the non-calculator papers, the final collections of questions will have an emphasis on skills typically tested in the calculator papers.

If you’re just getting started with Imvoto, we show how to use these questions in less than a minute with your Year 11s in a recent post.

Higher tier

The higher tier collections have been collated by our colleague, Mark Dawes. He’s been using these collections with his Year 11 pupils who are targeting A grades, although recently very many have been getting A*s on past papers. It’s important to note that the questions cover ‘easier’ topics too: it’s vital that pupils gain marks earlier in the paper if they are to achieve the highest grades.

Mark has been assigning the questions to his pupils as “optional homework”. Pupils have been impressively keen and a majority of his class are completing them every day.

All of the higher tier questions are already written and published and you can find them on the Imvoto site with this search. However, we’ll also be updating this list and our Twitter feed daily to indicate which topics are covered in that day’s questions.

  • A: Saturday 30 April 2016: standard form; indices; problem solving (meter reading); nth term of linear sequence.
  • B: Sunday 1 May 2016: straight line graphs; aea of circle; circle thorems; prime factors
  • C: Monday 2 May 2016: expand and simplify; Pythagoras; nets of cube; bearings; simplify expression
  • D: Tuesday 3 May 2016: bracket squared; “recycled” calculation; speed; tiles; conditional probability
  • E: Wednesday 4 May 2016: standard form; expand double brackets; recipe; sampling; substitute into expression
  • F: Thursday 5 May 2016: midpoint; estimates; fractional index; length of line segment; bounds.
  • G: Friday 6 May 2016: adding fractions; area of isosceles triangle; solve equation with brackets; area of semi-circle; % discount
  • H: Saturday 7 May 2016: solve quadratic equation; bounds; circle theorem; compound interest; quadratic substitution.
  • I: Sunday 8 May 2016: product of prime factors; simultaneous equations; sector area; average speed; recycled calculation.
  • J: Monday 9 May 2016: interior angles; length of line segment; converting volume; trig find length; mean from frequency table.
  • K: Tuesday 10 May 2016: simplify by collecting terms; cyclic quadrilateral; questionnaires; bounds; highest common factor.
  • L: Wednesday 11 May 2016: using a calculator; rounding to 3 significant figures; area problem solving; exterior angle; divide into 3-part ratio
  • M: Thursday 12 May 2016: proportion; compound interest; solve quadratic using formula; perimeter of semicircle; probability without replacement.
  • N: Friday 13 May 2016: solve inequality; zero power; multiply fractions; expand bracket with surds; interior angles of regular decagon
  • O: Saturday 14 May 2016: angles problem solving (×2); recurring decimal to fraction; area of equilateral triangle; probability expectation
  • P: Sunday 15 May 2016:  product of prime factors; RA trigonometry (find side); perimeter of sector; nth term; reverse percentage.
  • Q: Monday 16 May 2016: division of fractions; area of triangle via trig; train tickets; inverse proportion; ordering areas.
  • R: Tuesday 17 May 2016: factorise fully; solve quadratic not equal to zero; highest common factor; comparing areas; probability without replacement.
  • S: Wednesday 18 May 2016: vectors; sine rule; correlation; highest common factor; standard form.
  • T: Thursday 19 May 2016: density; ordinary form; power 0.5; simplify indices;  division of mixed number.
  • U: Friday 20 May 2016: expectation; speed with standard form; area of triangle with surds; trigonometry with surds; volume of sphere.
  • V: Saturday 21 May 2016: standard form; evaluate negative power; add fractions; probability expectation; speed in standard form.
  • W: Sunday 22 May 2016: trigonometry (find angle); lowest common multiple problem; angles in triangle with parallel lines; equation of line; integer solutions to inequality.
  • X: Monday 23 May 2016: % discount; comparing boxplots; circle theorem; bearings; recurring decimal to fraction.
  • Y: Tuesday 24 May 2016: kg to tonnes conversion; trigonometry problem; quadratic simultaneous equations; nth term of sequence; range from stem and leaf.
  • Z: Wednesday 25 May 2016: averages problem solving; circle theorem; circle area; ÷ of fractions; bracket to a power.
  • a: Thursday 26 May 2016: y=mx+c; LCM; area of triangle with trig; standard form km to cm conversion; perimeter of sector.
  • b: Friday 27 May 2016: expand brackets; interior angles of regular octagon; estimate answer; solve inequality; speed.
  • c: Saturday 28 May 2016: factorise fully; lowest common multiple; bounds (area); median from S&L; conditional probability.
  • d: Sunday 29 May 2016: diagonal of square to area; integer solutions of inequality; expand double brackets; ratio problem; circle theorem.
  • e: Monday 30 May 2016: solve simultaneous equations; standard form ×; circle area to radius; simplify ÷ with indices; volume of prism.
  • f: Tuesday 31 May 2016: reverse percentage; solve quadratic; area of compound shape; rhombus vectors; conditional probability.
  • g: Wednesday 1 June 2016: expand brackets; surface area of prism; factorise quadratic; trig (find angle); circle theorem.
  • h: Thursday 2 June 2016: simplify inequality; bounds from perimeter; Pythagoras; area of equilateral triangle; converting cubic units.
  • i: Friday 3 June 2016: find % increase; area of circle; expand brackets; product of prime factors; recurring decimal to fraction.
  • j: Saturday 4 June 2016: area of sector; scale drawing; carpet tiles problem; area of triangle (trig); highest common factor.
  • k: Sunday 5 June 2016: mean of grouped data; expression in context; square units conversion; circle theorem; vector.
  • l: Monday 6 June 2016: stratified sample; problem solving; bicycle wheel; area of triangle (trig); probability.

Foundation tier

The foundation tier collections have been written with Jamie’s class in mind: pupils aiming for that all-important C grade.

Many of the pupils in this group have difficulty with retention of terminology. As a result, each day’s collection will feature at least one question that you might expect to see within the first few pages of a GCSE paper.

These questions will be released each day and the list below will indicate the topics covered:

  • A: Saturday 30 April 2016. Simplifying algebra by collecting terms; decimal to percentage conversion; generating a sequence from nth term rule; substitute into algebraic expression; angle nomenclature.
  • B: Sunday 1 May 2016: naming angles; angle sums; mean from frequency table; sensible probabilities; equivalent fractions.
  • C: Monday 2 May 2016: estimation; percentage to fraction; expanding brackets; corresponding angles; pie chart angles
  • D: Tuesday 3 May 2016: % increase; solve equation; coordinates; symmetry; circle nomenclature.
  • F: Thursday 5 May 2016: names of polygons; median from raw data; angles in triangles; simplifying ratios; probability.
  • G: Friday 6 May 2016: place value; reading scales; angles on straight line; rounding to dp; naming triangles.
  • H: Saturday 7 May 2016: factors and multiples; % of amount; metric conversion; simplify ratio with units.
  • I: Sunday 8 May 2016: reading a timetable; significant figures; stem and leaf range; gradient; sharing in ratio.
  • J: Monday 9 May 2016: area of trapezium; equation with brackets; volume of prism; edges of cuboid; mutually exclusive events.
  • K: Tuesday 10 May 2016: line of symmetry; cuboid vertices; opposite angles; circumference; inequality solutions.
  • L: Wednesday 11 May 2016: square root; decimal multiplication; area of triangle; circle names; mode from freq table.
  • M: Thursday 12 May 2016: balancing fractions; describing correlation; similar triangles; octagon perimeter; reading scales
  • N: Friday 13 May 2016: scatter graph relationship; perimeter; perimeter of tessellation; sensible units; probability expectation.
  • O: Saturday 14 May 2016: vertices of solid; rounding to significant figures; cube root; problem solving with rectangle; midpoint.
  • P: Sunday 15 May 2016: simplify fraction; solve perimeter equation; mode from frequency table; change subject of formula; indices ÷.
  • Q: Monday 16 May 2016: conversion graph; bearings; division with negatives; angles around point; solve equation.
  • R: Tuesday 17 May 2016: pictogram; reflex angle; evaluate cube number; vertically opposite angles; area of triangle.
  • S: Wednesday 18 May 2016: exterior angle; symmetry; speed; equation of line; factorise expression.
  • T: Thursday 19 May 2016: reading decimal scale; order of operations; mode from S&L; ratio problem; expand brackets and collect terms.
  • U: Friday 20 May 2016: circle names; volume of cuboid; solve linear equation; probability; division.
  • V: Saturday 21 May 2016: 12-gon perimeter; edges from a net; gradient; bearings; triangle angles.
  • W: Sunday 22 May 2016: factorise expression; angle in triangle; multiply mixed numbers; volume of cylinder; lowest common multiple problem.
  • X: Monday 23 May 2016: money problem; area/perimeter problem; decimal division; substitution (brackets); range from stem and leaf.
  • Y: Tuesday 24 May 2016: order of operations; km to m conversion; vertically opposite angles; division of fractions; integer solutions to inequalities.
  • Z: Wednesday 25 May 2016: reading from scale; negative temperatures; perimeter on grid; perimeter with fractions; cooking a chicken.
  • a: Thursday 26 May 2016: using calculator; rhombus properties; mean of raw data; substitution of negatives and decimals; area of triangle.
  • b: Friday 27 May 2016: place value; trapezium; exterior angle of quadrilateral; probability; area problem.
  • c: Saturday 28 May 2016: decimal square root; passengers on a bus; decimal to fraction; circumference of circle; factorise area expression.
  • d: Sunday 29 May 2016: money problem; factors of 12; difference of temperatures; filling a fuel tank; substitute negative values.
  • e: Monday 30 May 2016: probability; square numbers; pay rise; using calculator; conversion graph.
  • f: Tuesday 31 May 2016: factors; median; compound circle area; number line inequality; similar triangles.
  • g: Wednesday 1 June 2016: metric reading from scale; using calculator; expand and simplify; mean of raw data; decagon side length.
  • h: Thursday 2 June 2016: l->ml conversion; rounding to significant figures; order of line symmetry; hiring a plumber.
  • i: Friday 3 June 2016: rounding to nearest 100; (bi)modal value from raw data; fractions with calculator; perimeter from area (algebraic); % increase.
  • J: Saturday 4 June 2016: correlation; solve equation; decimal multiplication; bus queue; cube root with calculator.
  • l: Monday 6 June 2016: halfway between; % of amount; rhubarb recipe; mean of grouped data; form expression.