End-of-year maths revision for P1 to Sec 4

Primary 1 maths: end-of-year revision

Topic: End-of-year revision (Select 8) – a mixed set of word problems that pulls together what your child has learnt this year.

• -Solve “more than” and “fewer than” stories, e.g. Peter scored 9 more marks for English than for Chinese
• -Find the total altogether after working out one part first
• -Tell the time by picking the clock that shows a time between 10 and 11 o’clock
• -Choose the right coins to pay 85 cents, and compare sets of money to find the greatest and smallest amounts
• -Work out which two items John bought from the notes he paid, a simple reasoning puzzle
• -Find the amount at first, or how much more is needed, e.g. saving up for a $73 bicycle
• -Solve two-step problems, such as ribbons bought and then used to make a dress
• -Fill in missing numbers

Primary 2 maths: shapes

Topic: Shapes – recognising, counting and building flat and solid shapes, plus problem sums.

• -Name the basic shapes (rectangles, triangles, circles and quarter circles) used to make a figure
• -Count the shapes hidden inside a larger figure, e.g. how many triangles there are
• -Draw lines to split a figure into given shapes, e.g. 1 rectangle and 3 triangles
• -Tell straight lines and curves apart, and count each in a figure
• -Spot flat and curved surfaces on solids, e.g. the faces of a cylinder
• -Name 3D shapes: cube, cuboid, cylinder and sphere
• -Continue shape patterns by drawing the next shape
• -Use the “suppose all are” method for legs and wheels problems, e.g. cows and ducks on a farm
• -Draw models to compare and add amounts of money

Primary 3 maths: end-of-year exam revision

Topic: End-of-year exam revision (Select 12) – a mixed set of problem sums covering the main P3 topics.

• -Find the area and perimeter of squares, rectangles and overlapping figures
• -Compare angles with a right angle
• -Solve multiplication and division problems, e.g. muffins packed equally into boxes
• -Use substitution, e.g. 9 chairs are as heavy as 6 desks
• -Work with money: menu prices, coins in a purse, and how much more is needed
• -Find time taken and start or finishing times, e.g. a train journey between towns
• -Draw models for “more than” and sum-and-difference problems
• -Use place value to make the smallest 4-digit odd number from given digits
• -Solve fencing and running perimeter problems, e.g. 7 rounds of a rectangular field

Primary 4 maths: end-of-year exam revision

Topic: End-of-year exam revision (Select 13) – exam-style questions across P4 topics.

• -Read bar graphs, tables and a pie chart of children’s favourite colours
• -Solve before-and-after problems where equal amounts are spent or the same number of items is sold, e.g. Shop A ends up with 5 times as many books as Shop B
• -Draw models for age problems and money received
• -Find the area and perimeter of composite figures, including fencing costs and carpets on a floor
• -Continue decimal and letter patterns, e.g. the letter on the 78th card
• -Estimate products and round off to the nearest hundred
• -Work out total cost from bundle prices, e.g. 3 oranges for $4.55
• -Complete figures using lines of symmetry
• -Use common multiples to find when coloured lights light up together

Primary 5 maths: end-of-year exam revision

Topic: End-of-year exam revision (Select 15) – challenging problem sums across the P5 syllabus.

• -Solve before-and-after money transfers using models and units
• -Solve rate problems with two teams painting walls at different speeds
• -Use grouping for equal numbers of donuts and cupcakes, and for 10-cent, 20-cent and 50-cent coins
• -Find the areas of triangles that share the same height
• -Draw the top and side views of a solid made of cubes
• -Calculate GST on a discounted price, and the percentage of a salary spent and saved
• -Find unknown angles in trapeziums, rhombuses and parallelograms
• -Solve age problems and a ring-toss game with bonus points
• -Round decimals to 2 decimal places, and find the volume of water needed to fill a tank

Secondary 1 maths: end-of-year exam revision

Topic: End-of-year exam revision (Select 15) – exam-style questions across the Secondary 1 syllabus.

• -Apply rounding in real life: a supermarket’s price-rounding rule and how much is saved on one receipt
• -Simplify algebraic fractions into a single fraction, and factorise expressions
• -Form algebraic expressions for the perimeter of a rectangle and a triangle
• -Compare best buys by average cost per bottle, and state the assumption made
• -Use ratio and fractions to find the smallest possible number of counters
• -Convert speed to km/h using a real SEA Games swimming record, and work out average speed
• -Read rate of savings from the gradient of a graph
• -Find the sum of interior angles of polygons
• -Use density, mass and volume for a metal cuboid, and fit cuboids into a cube container
• -Read a data table and find the area and perimeter of a shaded region

Secondary 2 maths: end-of-year exam revision

Topic: End-of-year exam revision (Select 12) – exam-style questions across the Secondary 2 syllabus.

• -Use algebraic identities to spot a perfect square and find a ratio
• -Solve quadratic equations by factorising, including one formed from a word problem on selling vases
• -Apply inverse proportion to find the percentage change in printing time
• -Use similar triangles and Pythagoras’ theorem to find unknown lengths
• -Find unknown values from the mode, median and mean of a frequency table
• -Apply trigonometry to a ladder leaning against a wall, and to angles between mountain peaks
• -Use inequalities in a geometry problem, rounding correctly to 3 significant figures
• -Work with map scales for both distance and area
• -Use density and volume to find how many spheres raise the water level in a tank

Secondary 3 maths: end-of-year exam revision

Topic: End-of-year exam revision (Select 15) – exam-style questions across the Secondary 3 syllabus.

• -Use coordinate geometry to find the length of a line segment
• -Read speed-time graphs, using the gradient for speed and working out distance travelled, then sketch the matching distance-time graph
• -Apply the sine rule and cosine rule to bearings and the area of a plantation
• -Find angles of depression from a point halfway up a pole
• -Find areas of shapes built from semicircles and quadrants
• -Work with number patterns, and read the least value from a graph
• -Solve simultaneous equations by comparing coefficients and substitution, and substitute values into formulae
• -Use map scales for actual distance and area, and standard form, e.g. the mass of an electron

Secondary 3 Additional Maths: end-of-year exam revision

Topic: Final revision 1 – Algebra (Select 15) – exam-style Additional Mathematics questions.

• -Use completing the square to find the turning point of a curve, and whether it is a maximum or minimum
• -Explain why a graph has no x-intercepts, and find the turning point of a related curve
• -Use the discriminant to find ranges of values, the condition for a line to be a tangent to a curve, and to show an equation always has real roots
• -Solve quadratic inequalities
• -Work with surds: rationalise denominators and express answers in the form a + b√2
• -Apply the remainder and factor theorems to find unknown coefficients, then factorise a cubic completely
• -Use the sum and difference of cubes
• -Express a fraction as partial fractions, including a repeated factor

Secondary 4 maths: O-Level final revision

Topic: Final revision 2 – Number and Algebra, Geometry and Measurement (Select 30) – exam-style Secondary 4 Mathematics questions.

• -Find the nth term of number patterns, and explain why a term is always even or a multiple of 3
• -Shade Venn diagrams and count elements in sets
• -Use matrices in a real-life sales problem, and explain what each result means
• -Find interior and exterior angles of polygons, including a regular hexagon
• -Apply circle properties: angles in a semicircle, tangents, angles at the centre and in opposite segments
• -Prove triangles similar or congruent, and use similar triangles to find the width of a canal
• -Express vectors in terms of a and b, and compare areas using ratios
• -Find the volume of a frustum, and how many ball bearings make the water overflow

Secondary 4 Additional Maths: O-Level final revision

Topic: Final revision 2 – Geometry and Trigonometry (Select 22) – exam-style Additional Mathematics questions.

• -Use coordinate geometry: gradients, perpendicular lines and bisectors, and finding the missing corner of a quadrilateral
• -Work with circles: find the equation of a circle and of a tangent, and the points where a straight line meets a circle
• -Apply linear law: turn P = Ab^T into a straight-line graph, use its gradient and intercept to find the constants, then read values from the graph
• -Find trigonometric values such as tan x without a calculator, using the quadrant the angle lies in and a right-angled triangle
• -Read trigonometric graphs to find the amplitude, period and constants, and count the number of solutions
• -Solve trigonometric equations within a given range, checking which quadrants the answers fall in