Algebra

Simplify fully 8m + 4 - 2m + 7

Simplify fully (1/2)c × 6d

Complete this number machine so that y = 4x + 5

Complete this number machine so that y = 3x - 24

Complete this number machine so that y = x

Write the missing term in the geometric progression. 1, 4, 16, __, 256

A Fibonacci-type sequence begins 5, -9, ... The sequence is continued by adding the previous two terms. Work out the next two terms.

Solve 7x - 22 = 4x + 29

Represent -2 < x < 4 on the number line.

Solve 5y + 14 ≥ 11

4 chocolate bars and 3 packets of mints cost £4.70. 5 chocolate bars and 1 packet of mints cost £4.50. Work out the cost of a chocolate bar and the cost of a packet of mints.

Rearrange y = (3x + 7) / x to make x the subject.

A circle has centre O and passes through (0, 6). Write down the equation of the circle.

5x³ + ax² + bx + c ≡ kx³ + (2 - k)x² + (a² - 1)x + b/2 Work out the values of a, b and c.

The first three terms of a geometric progression are √5/2, 5/4, 5√5/8. Work out the next term.

The nth term of a sequence is (2 + √3)ⁿ. Show that the third term is 26 + 15√3.

9k + 7 and 2k² + 3 are consecutive integers. 9k + 7 is the smaller integer. Work out the value of the next consecutive integer.

Solve 5x = 30

Solve -2 + y = 10

Simplify fully (20w) / (4w)

Work out the value of x² + 7x when x = -4

Rearrange y = w - 1 to make w the subject.

Simplify fully 4(a + 2) + a

Here are three terms: xy, x², 5y². Alec multiplies two of these terms. Work out the three possible fully simplified answers.

Here is a number machine. Complete the number machine.

Here is a different number machine. Complete the number machine.

Here is a different number machine. When x = 5, y = 13 and when x = 10, y = 28 Complete the number machine.

Here are three terms. <br> xy, &nbsp; x², &nbsp; 5y² <br> Alec multiplies two of these terms. <br> Work out the three possible fully simplified answers.

Solve (x + 2)(x - 5) = 6x

Straight line LM has equation y = 4x - 7 <br> Straight line ST has equation y = (9 - x) / 4 <br> Are the lines LM and ST perpendicular? Yes or No. <br> Give a reason for your answer.

Here is a formula for an iterative process. <br> uₙ₊₁ = 24/uₙ + 4 <br> u₂ = 8 <br> Work out the values of u₁ and u₃.

The graph represents the velocity of a ball as it rolls along the ground. <br> Work out an estimate for the acceleration of the ball, in m/s², after 2 seconds. You must show your working.

The nth term of a sequence is n² - 30n + 236 <br> By completing the square, show that all the terms of the sequence have two or more digits.

The total cost of a taxi ride is calculated by adding a fixed charge of £4 and a charge of £2 per mile. Write a formula to work out the total cost, £C, of a journey of m miles.

A triangle is drawn using the lines y = x, x = -2, and y = 4. Work out the coordinates of the three vertices of the triangle.

Factorise fully 12t + 4t³

This question is about what happens to the value of y when the value of x is doubled in different equations. For the equation y = 8x, what happens to the value of y when x is doubled?

For the equation y = 10/x, what happens to the value of y when x is doubled?

For the equation y = 3x², what happens to the value of y when x is doubled?

Rearrange y = √( (x/2) + 1 ) to make x the subject.

Factorise fully 3x² + 23x + 30

The distance of a particle from a point is d metres after t seconds. The relationship is given by d = a × bᵗ where a and b are constants. Use the graph to work out the values of a and b.

A curve has the equation y = x² + 4x - 4. A straight line has the equation y = 3x - 2. Work out the two points of intersection of the curve and the straight line.