Year 11 Paper 3: Foundation Full Course Review

Question 1 [2 marks]

Number and Calculation

A stationery shop orders 34 boxes of pens. Each box contains 48 pens.

The shop already has 156 pens in stock. Work out the total number of pens now in the shop.

Question 2 [2 marks]

Functions and Rates of Change

The function f is defined by f(x) = x^2 - 3x.

Find f(-2).

Question 3 [2 marks]

Mensuration and Vectors

A triangle has base 16 cm and perpendicular height 7 cm. Find its area.

Question 4 [2 marks]

Number and Calculation

A youth club needs to transport 138 students to a trip.

Each coach seats 24 students. Find the minimum number of coaches needed.

Question 5 [3 marks]

Quadratics and Simultaneous Equations

Factorise completely 3x^2 + 9x - 84.

Question 6 [3 marks]

Linear Equations and Inequalities

Expand and simplify 3(2x - 5) + 4(x + 6).

Question 7 [3 marks]

Functions and Rates of Change

The function g is defined by g(x) = 2x^2 - 3.

Find g(-4).

Question 8 [4 marks]

Pythagoras and Trigonometry

In a right-angled triangle, the side opposite angle y is 9 cm and the side adjacent to angle y is 6.5 cm.

Find y to 1 decimal place.

Question 9 [4 marks]

Angles, Polygons and Circle Theorems

Three angles meet at a point. One angle is 130 degrees, another is 3x degrees and the third is 2x degrees.

Find the value of x, then state the size of the smallest of the three angles at the point.

Question 10 [4 marks]

Statistics and Probability

The prices, in pounds, of 6 items in a shop are 12, 15, 9, 18, 14 and 16.

Find the mean price. A seventh item priced at 30 pounds is then added to the list.

Find the new mean price of all 7 items.

Question 11 [4 marks]

Ratio and Proportion

A bag of 360 sweets is shared between Priya, Sam and Tom in the ratio 4:5:9.

Find the difference between Tom's share and Priya's share.

Question 12 [3 marks]

Linear Equations and Inequalities

Solve the inequality 4x + 7 < 2x + 19.

Question 13 [4 marks]

Functions and Rates of Change

The function g is defined by g(x) = x^2 - 2x.

Find the value of g(5) - g(-2).

Question 14 [4 marks]

Angles, Polygons and Circle Theorems

A, B and C are points on the circumference of a circle, where AC is a diameter.

Angle BAC = 34 degrees. Find angle ABC and angle BCA.

Question 15 [4 marks]

Statistics and Probability

A spinner has sections labelled A, B, C and D.

P(A) = 0.3, P(B) = 0.25 and P(C) = 0.2.

Find P(D).

Question 16 [4 marks]

Ratio and Proportion

In a school, the ratio of Year 10 students to Year 11 students is 5:4.

The ratio of Year 11 students to Year 12 students is 2:3.

Find the ratio of Year 10 to Year 11 to Year 12 students, in its simplest form.

Question 17 [4 marks]

Number and Calculation

Determine whether 259 is a prime number. Show your working.

Question 18 [4 marks]

Mensuration and Vectors

A circular pond has radius 6.5 m.

Find its circumference to 1 decimal place.

Question 19 [5 marks]

Angles, Polygons and Circle Theorems

A, B and C are points on the circumference of a circle with centre O.

B is on the major arc AC and angle AOC (the non-reflex angle at the centre) = 136 degrees.

Find angle ABC and angle OAC.

Question 20 [5 marks]

Quadratics and Simultaneous Equations

Solve 2x^2 - 5x - 12 = 0 by factorising.

Question 21 [5 marks]

Linear Equations and Inequalities

Tickets to a fair cost 6 pounds each, and there is a fixed 8 pound parking charge.

A family has a budget of 50 pounds.

Form an inequality and find the greatest number of tickets the family can buy without exceeding their budget.

Question 22 [5 marks]

Functions and Rates of Change

The function h is defined by h(x) = 3/(x - 2) for x is not equal to 2.

Find h^-1(x), and hence find h^-1(1).