Edexcel-Style Year 10 Higher Paper 2

Question 1 [1 marks]

Linear Algebra

Solve 5x = 35

Question 2 [1 marks]

Indices and Standard Form

Write 9.1 x 10^4 as an ordinary number.

Question 3 [1 marks]

Angles and Geometrical Reasoning

P, Q and R lie on a straight line. Angle a and an angle of 118 degrees lie on the same side of the line at Q.

Question 4 [2 marks]

Sequences

Here are the first four terms of a sequence. 3, 7, 11, 15

Write down the next term of the sequence.

Describe, in words, the term-to-term rule for the sequence.

Question 5 [2 marks]

Number and Calculation

The population of a town is 24 000, correct to 2 significant figures. Write down the error interval for the population, P.

Question 6 [3 marks]

Ratio and Proportion

Ayesha and Ben share £360 in the ratio 4:5. Work out how much money Ben receives.

Question 7 [1 marks]

Fractions, Decimals and Percentages

A number is decreased by 40% to give 54. Which calculation gives the original number?

Question 8 [2 marks]

Graphs and Coordinates

Explain why there is no point that can satisfy both y > 2x + 1 and y < 2x - 1. Give a short algebraic justification.

Question 9 [2 marks]

Area, Volume and Measures

Work out the circumference of a circle with radius 7 cm. Give your answer in terms of pi.

Question 10 [2 marks]

Fractions, Decimals and Percentages

The number of members of a gym increased by 12% this year. There are now 504 members. Work out the number of members last year.

Question 11 [5 marks]

Area, Volume and Measures

Cone G and cone H are mathematically similar. The base radius of cone G is 5 cm and the base radius of cone H is 8 cm. The surface area of cone G is 130 cm^2 and the volume of cone G is 150 cm^3.

Work out the surface area of cone H.

Work out the volume of cone H.

Question 12 [2 marks]

Linear Algebra

Show that x = 5, y = -2 satisfies both of the simultaneous equations: 3x + 2y = 11 2x - y = 12

Question 13 [2 marks]

Area, Volume and Measures

Work out the volume of a sphere with radius 5 cm. Give your answer in terms of pi.

Question 14 [2 marks]

Linear Algebra

Solve 6x - 5 = 19 Show your working.

Question 15 [3 marks]

Ratio and Proportion

Using 3 identical pumps, it takes 100 minutes to fill a swimming pool. The time taken, T minutes, is inversely proportional to the number of pumps used, n. Work out the minimum number of pumps needed to fill the pool in no more than 40 minutes.

Question 16 [3 marks]

Area, Volume and Measures

A cylinder has height 30 cm. The volume of the cylinder is 15000 cm^3. Diagram: cylinder labelled height 30 cm, radius r unknown. Work out the radius of the cylinder. Give your answer correct to 1 decimal place.

Question 17 [3 marks]

Angles and Geometrical Reasoning

A plane flies from airport A on a bearing of 060 for 100 km to reach point B. It then flies on a bearing of 150 for 100 km to reach point C. Diagram: Airport A, point B and point C are shown. AB = 100 km on a bearing of 060. BC = 100 km on a bearing of 150. North arrows are shown at A and B.

Question 18 [2 marks]

Area, Volume and Measures

Find the arc length of a sector with radius 10 m and central angle 72 degrees. Give your answer in metres, correct to 3 significant figures.

Question 19 [3 marks]

Fractions, Decimals and Percentages

Show that investing £800 at a compound interest rate of 5% per year gives a value of £882 after 2 years.

Question 20 [3 marks]

Graphs and Coordinates

Consider a vehicle with velocity described by: from t = 0 s to 3 s velocity increases uniformly from 0 to 6 m/s; from t = 3 s to 8 s velocity is constant at 6 m/s; from t = 8 s to 10 s velocity decreases uniformly from 6 to 0 m/s. State (a) the time interval when the vehicle is speeding up, (b) the interval when the vehicle moves at constant speed, and (c) the interval when the vehicle is slowing down.

State the time interval when the vehicle is speeding up.

State the time interval when the vehicle moves at constant speed.

State the time interval when the vehicle is slowing down.

Question 21 [4 marks]

Area, Volume and Measures

Two solid bronze statues are mathematically similar. The height of the smaller statue is 30 cm and its mass is 12 kg. The height of the larger statue is 45 cm. The statues are made from the same bronze, so mass is proportional to volume.

Question 22 [4 marks]

Fractions, Decimals and Percentages

A school fundraiser collected £840. The organisers decide to give 12% to charity, use 35% for equipment, and split the remainder equally between two sports teams. Work out how much each sports team receives. Show your working.

Question 23 [2 marks]

Angles and Geometrical Reasoning

v is the column vector (9, 12). Calculate the magnitude of v, |v|.

Question 24 [5 marks]

Area, Volume and Measures

The minute hand of a clock is 8 cm long. Calculate the area swept out by the minute hand in 25 minutes, giving your answer correct to 3 significant figures.

Question 25 [2 marks]

Linear Algebra

Prove algebraically that the product of any two even numbers is always a multiple of 4.

Question 26 [3 marks]

Area, Volume and Measures

Funnel P and funnel Q are mathematically similar. The volumes of funnel P and funnel Q are in the ratio 27:1000. The slant height of funnel P is 9 cm. Work out the slant height of funnel Q.

Question 27 [3 marks]

Linear Algebra

Solve x^2 - 5x - 14 = 0 by factorising. Show your working.

Question 28 [3 marks]

Sequences

The nth term of a sequence is 6n - 1. Prove algebraically that the sum of any three consecutive terms of this sequence is always a multiple of 3.

Question 29 [4 marks]

Fractions, Decimals and Percentages

A shop increases the price of a coffee machine by 30%, then reduces this new price by 30% in a clearance sale. The final sale price is £109.20. Work out the original price of the coffee machine, and state whether the final sale price is greater than, less than, or equal to the original price.

Question 30 [5 marks]

Linear Algebra

The time, T seconds, taken for a ball dropped from height h metres to hit the ground is given by the formula T = sqrt(2h/g), where g is the gravitational field strength.

Make h the subject of the formula.

A ball is dropped from a window and takes exactly 2 seconds to hit the ground. Use g = 9.8 m/s^2 and your formula from part (a) to work out the height of the window above the ground.