Samples

A few worksheets we've made.

Print-ready worksheets you can download and inspect. Every question comes with a worked solution.

E-Math

1.(a) Expand and simplify (2x − 3)(x + 5) − (x − 4)². [3] (b) Factorise completely 6xy − 9y + 4x − 6. [2] (c) Solve 2x² − 1x − 3 = 0. [2]
2.(a) Simplify (x² − 9) / (3x² + 12x + 9). [3] (b) Given that y = (5x − 2) / (x + 3), make x the subject of the formula. [3]
3.(a) Express y = x² − 4x − 10 in the form y = a(x + b)² + c, where a, b and c are constants. [3] (b) Hence state the coordinates of the turning point of the curve. [1]

E-MathAlgebraMedium

Algebra: Expansion, Factorisation & Equations

3 questions · worked solutions included

E-Math

1.The variables x and y are connected by y = x³ − 4x + 3. Some corresponding values of x and y are given in the table. | x | -2 | -1 | 0 | 1 | 2 | 3 | |---|----|----|---|---|---|---| | y | 3 | 6 | 3 | 0 | 3 | 18 | (a) Calculate the value of y when x = 2. [1] (b) Using a scale of 2 cm to 1 unit on the x-axis and 1 cm to 2 units on the y-axis, draw the graph of y = x³ − 4x + 3 for -2 ≤ x ≤ 3. [3] (c) Use your graph to find the values of x for which x³ − 4x + 3 = 0. [2] (d) By drawing a tangent, estimate the gradient of the curve at the point where x = 2. [2] (e) By drawing a suitable straight line on the same grid, solve the equation x³ − 4x + 3 = 3x − 1. [3]
2.The curve y = x² + 8x + 3 is given. (a) Express y = x² + 8x + 3 in the form (x + 4)² + -13. [2] (b) State the coordinates of the turning point. [1] (c) State the equation of the line of symmetry. [1]
3.The points A(-3, 1) and B(1, 5) lie on a coordinate plane. The point C(5, 8) lies above the line AB. (a) Find the equation of the line AB in the form y = mx + c. [2] (b) Find the equation of the line through C parallel to AB. [2] (c) Find the coordinates of the intersection of the line from part (b) with the line y = -1x + -5. [2] (d) Find the length of AB, leaving your answer in surd form. [2]

E-MathFunctions & GraphsMedium

Functions & Graphs

3 questions · worked solutions included

E-Math

1.In the diagram, A, B, C, D lie on a circle centre O. TA is tangent to the circle at A. Angle ADC = 118° and angle BAT = 40°. Find, giving a reason for each answer, (a) angle ABC. [2] (b) angle ACB. [2] (c) reflex angle AOC. [2]
2.In the diagram, angle ACB = angle DAB, AB = 6 cm and BC = 2 cm. (a) Show that △ABC and △DBA are similar. [2] (b) Find the length of CD. [2] (c) Given that the area of △DBA is 36 cm², find the area of △ABC. [2]
3.Two concentric circles have centre O. PQ is a diameter of the larger circle and RS is a diameter of the smaller circle. PS and RQ are tangents to the smaller circle. The radius of the larger circle is 17 cm and the radius of the smaller circle is 8 cm. (a) Show that △PSO ≅ △QRO, stating your reason clearly. [2] (b) Calculate the area of △QRO. [3]

E-MathGeometryMedium

Geometry: Angles, Circles & Proof

3 questions · worked solutions included

E-Math

1.In a horizontal triangle ABC, AB = 20 m, BC = 30 m and angle ABC = 95°. (a) Calculate the length of AC. [2] (b) Calculate angle BAC. [2] (c) Find the shortest distance from B to AC. [2] (d) A vertical flagpole of height 12 m stands at A. A person walks along BC. Find the greatest angle of elevation of the top of the flagpole from a point on BC. [3]
2.Three points P, Q, R lie on horizontal ground. Q is due east of P with PQ = 60 m. The bearing of R from P is 45° and the bearing of R from Q is 315°. (a) Find angle QPR, angle PQR and angle PRQ. [2] (b) Find the distance QR. [3] (c) Find the area of triangle PQR and the shortest distance from R to PQ. [2]
3.A sector OAB has centre O and radius 15 cm. Angle AOB = 1.2 radians. M is the midpoint of OB. A line from A to M divides the sector into two regions. (a) Find the length of arc AB. [1] (b) Find the area of sector OAB. [2] (c) Find the length of AM. [2] (d) Find the area of the smaller region (bounded by arc AB, the line AM, and part of OB). [3]

E-MathMensuration & TrigMedium

Mensuration & Trigonometry

3 questions · worked solutions included

E-Math

1.Mrs Tan exchanges SGD 2500 for Malaysian ringgit at 1 SGD = 3.00 MYR. He spends MYR 3000 on accommodation and food, and buys 100 litres of fuel at MYR 2.40 per litre. He exchanges the remaining MYR back at 1 SGD = 3.10 MYR and receives SGD 80. (a) Calculate the MYR remaining before he converted back. [2] (b) Show, with working, whether he has enough to cover the return trip (assume same fuel needs). [2] (c) A bank offers the conversion at 1 SGD = 2.95 MYR but charges a 1.5% conversion fee. Compare this against the original rate and justify which is better. [3]
2.A home appliance shop buys a air fryer at a cost price. The shopkeeper marks up the cost price by 50% and lists it at a marked price of $1200. During a sale, the air fryer is sold at a 30% discount on the marked price, and the shopkeeper still makes a profit of 5% on the cost price. (a) Find the marked price of the air fryer. [Already given as $1200; verify by computation.] [1] (b) Find the selling price after the discount. [1] (c) Find the original cost price of the air fryer. [2]
3.Mdm Noor invests a principal of $10000 with OCBC at 4% per annum compounded yearly for 5 years. (a) Write down the formula for the total amount A after n years in terms of P and r. [1] (b) Calculate the total amount in the account after 5 years, giving your answer correct to the nearest cent. [3]

E-MathNumbers & RatioMedium

Numbers, Ratio & Proportion

3 questions · worked solutions included

E-Math

1.A survey records the lengths, x cm, of 100 fish. Grouped frequency table (class width 10 cm; upper bounds 10, 20, 30, 40, 50, 60): 0 < x ≤ 10: 20; 10 < x ≤ 20: 19; 20 < x ≤ 30: 13; 30 < x ≤ 40: 15; 40 < x ≤ 50: 15; 50 < x ≤ 60: 18. (a) Copy and complete the cumulative frequency table. [1] (b) On the grid, draw a cumulative frequency curve. [2] (c) Use your curve to estimate the median, the interquartile range, and the 20th percentile. [4] (d) A fish is considered "oversized" if their length exceeds 30 cm. Find the number of oversized fish. [2] (e) In a second survey of 100 fish at a different site, the values had the same median but a larger interquartile range. Describe how the cumulative frequency curve for this second survey would differ from the curve drawn in (b). [2]
2.Box-and-whisker plots show the length (cm) of fish kept in two tanks. Tank A: min 42, Q1 49, median 53, Q3 60, max 66. Tank B: min 44, Q1 48, median 49, Q3 53, max 58. There are 7 fish in Tank A with length greater than 60 cm. (a) Find the total number of fish kept in Tank A. [1] (b) Make one comment comparing the averages and one comment comparing the spread of the lengths in the two tanks. Use figures to support your answers. [4] (c) A third tank Tank C has fish with the same median as Tank B but a smaller interquartile range than both Tank A and Tank B. Sketch a possible box plot for Tank C on the same scale. [2]
3.A box contains 6 white balls and 7 black balls, making 13 balls in total. Two balls are drawn from the box at random, one after the other, without replacement. (a) Complete the probability tree diagram showing the two balls drawn and the corresponding probabilities. [2] (b) Find the probability that the two balls drawn are of the same type. [2] (c) Find the probability that at least one of the two balls drawn is white. [2] (d) The two balls are returned to the box and a third ball is drawn at random. Given that the first two balls drawn were both black, find the probability that the third ball drawn is white. [1]

E-MathStatistics & ProbabilityMedium

Statistics & Probability

3 questions · worked solutions included