26 questions · 100 marks · ≈ 2 hours
Calculator not allowed · Answer all questions · Show all your working
Ali, Beth and Chari pay rent on a piece of woodland. The annual rent that they pay is such that the amount Ali pays : the amount Beth pays : the amount Chari pays = 13 : 8 : 11 The amount that Chari pays = $2563 Calculate how much more rent Ali pays than Beth pays. $
Simplify fully 8 x + 12
Without using a calculator and showing all your working, evaluate 1 3 5 ÷2 3 5 Give your answer as a mixed number in its simplest form.
Ashley takes 3 hours and 36 minutes to walk around a lake. The distance she walks is 11 520 m. Calculate Ashley’s average speed. Give your answer in kilometres per hour kilometres per hour
Liam started a new job on a salary of $45 500 At the end of 1 year he is given a pay increase of 5.5% At the end of each subsequent year he is given a pay increase of 1.25% Calculate, to the nearest $, Liam’s salary at the end of 3 years after he started the job. $
The straight line L has equation 2y – 5 = 3x
Find the gradient of L
Find the coordinates of the point where L meets the y-axis. ( …………… , …………… )
Arthur has 10 cards. Each card has a letter on it and the letters spell the word PICCADILLY P I C C A D I L L Y Arthur selects at random 3 of these cards. Calculate the probability that he selects P A L in that order.
Without using a calculator and showing all your working, solve the inequality 6x2 – x – 12 > 0
The function f is defined by 3x f :xα x ≠ −2 2( x + 2) Express the inverse function f –1 in the form f –1 : x ↦ ... f –1 : x ↦
Without using a calculator and showing all your working, express 2+ 8 in the form a + b where a and b are integers.
Given that –3x2 + 6x + 2 can be written in the form a(x + b)² + c where a, b and c are integers, find the value of a, the value of b and the value of c. a = b = c =
The incomplete table and pie chart below show information about the favourite type of chocolate of 440 adults.
| Type of chocolate | Number of adults |
|---|---|
| Milk | 209 |
| Plain | |
| White | |
| Total | 440 |
Complete the table and the pie chart.
Here is information about the age, in years, of each of Jelina’s five children when written in order. b a b + a 2b + a + 3 2b + a + 5 It is given that a is the age of the youngest child a ≠ b two of the children have the same age the mean age of the five children is 10.6 years Calculate the value of a and the value of b Show clear algebraic working. a = b =
The diagram shows a triangle ABC. The point D lies on AC so that BD is perpendicular to AC. ∠BAD = 64° ∠ ACB = 28° AD = 2 cm Calculate the length, in cm to one decimal place, of BC cm
Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: B, A, D, C · Figure values: 64°, 28°, 2.
A=⎜ B=⎜ 2 − 4 2 2 −2 Calculate 3A – 2B 5 −3⎞ ⎛ 0 1⎞
P= QP −1 = −3 2 −10 −17 Find the matrix Q
The diagram shows a circle JKML. JKP and LMP are straight lines. JK = 3 cm, KP = 2.5 cm and PM = 2 cm. ∠JPL = 74° Calculate the area, in cm² to 2 decimal places, of triangle LKP cm²
Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: P, K, J, M, L · Figure values: 2.5, 74°, 2, 3.
Write 0.0234 in standard form.
Write 2.40 × 10⁵ as an ordinary number.
Calculate, giving your answer in standard form
(2.5 × 10¹⁰¹) ÷ (5 × 10⁻⁹⁸)
Show your working clearly.
Simplify 3w7y–3 × 4w2y3 4 2
Simplify (25x )
The diagram shows triangle ABC and triangle ADC. E is the point on BC and AD. F is the point on AC such that AB, FE and CD are parallel. Given that AB = 3 cm and that CD = 7 cm, calculate the length of FE cm
Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: D, B, E, A, F, C.
The diagram shows quadrilateral ABCD. The region R consists of all the points inside the quadrilateral that are
B A D The diagram shows quadrilateral ABCD. The region R consists of all the points inside the quadrilateral that are (i) closer to DA than to DC, (ii) less than 3 cm from the side DC, (iii) more than 4 cm from B. Using ruler and compasses only and showing all your construction lines, construct and show, by shading, the region R. Label the region R.
Figure not shown in this reconstruction — the printed paper includes a diagram. Labels in the original figure: C, B, A, D.
x° E D x° C A B The diagram shows a shaded 7-sided shape ABCDEFG. The points A, B, C, D, E, F and G are 7 vertices of a regular polygon with 11 sides. ∠GAB = ∠AGF = x° Calculate the value, to 3 significant figures, of x. Show your working clearly. x =
Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: G, F.
A B 4 cm 4 cm 76° Diagram NOT accurately drawn O C The diagram shows a sector OACB of a circle, centre O. OA = OB = 4 cm Angle AOB = 76°
Calculate the area, in cm² to 3 significant figures, of the shaded sector OACB
…………… cm²
Calculate the perimeter, in cm to 3 significant figures, of the shaded sector OACB cm
y is directly proportional to x³ x is inversely proportional to the square root of w. y = 729 when x = 4.5 x = 25 when w = 0.16 Find a formula for y in terms of w.
(2x + 1), (10x – 10) and (35x – 5) are the first three terms of a sequence. The first term of the sequence is (2x + 1) where (2x + 1) ≠ 0 After the first term, all other terms of the sequence are found by using the rule ‘multiply the previous term by d’ Given that x is an integer, find the value of d. d =
ABC is a triangle. → ⎛ 3⎞ → ⎛ x⎞ → AB = BC = where x > 0 and |AC| = 5 ⎝ −2⎠ ⎝ 5 x⎠ → Find AC as a column vector. Show clear algebraic working.
Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: C, A, B.
A small ball is thrown into the air from a point that is 1 m above horizontal ground. The ball moves vertically upwards so that at time t seconds after the ball was thrown, the height, h metres, of the ball above the ground is given by h = 1 + kt – 5t2 where k is a constant. At time t seconds after the ball was thrown, the velocity of the ball is v m/s.
Find an expression for v in terms of k and t. Given that the total distance travelled by the ball between the instant when the ball is thrown and when it hits the ground for the first time is 161 m …………… , ……………
calculate the value of k. k =