Questions and Answers of Complete Pure Mathematics

Express each of the quadratic equations in the form y = a (x + b)² + c.Sketch the curve, stating the coordinates of the vertex and whether there is a maximum orminimum value of y. y = x² +
Solve each of these quadratic equations. Give your answers as exact answers.a) x4 – 4x² – 21 = 0b) 6x4 – x² = 2c) x6 + 7x³ + 10 = 0d) 4 + 11x² – 3x4 = 0e) 6x8 + 6 = 13x4f)x6 + 3x³
Solve each of these quadratic equation.a) x² + 2x – 35 = 0b) x2 – 7x + 10 = 0c) x² – x – 12 = 0d) x² + 8x – 9 = 0e) x² – 3x = 18f) x² = x + 6 g) 0 = x² + 8x + 12h) 5x + x2
Work out the discriminant for each equation and then determine whether each equation has two distinct roots, equal roots or no real roots.a) 2x² – 3x + 4 = 0b) 5x² – 11x + 4 = 0 -c) x² + 12x +
Solve (6x − 5)(4 − 3x) = 0.
Solve these simultaneous equation.y = x + 1y = x² − 1
Solve these simultaneous equation.y = 4x + 7y = 2x² + 1
A rectangle has length (x + 4) cm and width (3x + 4) cm. The area of the rectangle is 11 cm². Find x.
Solve each of these inequalities. Sketch the curve for each, showing the interval that satisfies each inequality.a) x² + 7x + 12 ≤ 0b) x² – x – 30 < 0c) x² + 2x – 48 > 0
Solve each of these equations by completing the square. Leave your answers in surd form.a) x + 6x + 1 = 0b) x² – 4x – 8=0 c) 4 – 2x – x² = 0d) x2 – 20x + 30 = 0e) 3 + 8x – x² =
Use the formula to solve each of these quadratic equation. Leave your answers in surd form.a) 2x² – x – 5=0b) 3x² – 6x + 1 = 0c) 5x² – 3x – 7=0d) 6x² – x – 4 = 0e) x2 + 8x – 3 =
Express each of the quadratic equations in the form y = a (x + b)² + c. Sketch the curve, stating the coordinates of the vertex and whether there is a maximum or minimum value of y. y = x²
Solve each of these equation by completing the square. Write your answers correct to 2 decimal places.a) x6 – 8x³ + 1 = 0b) 3 – 6x² – x4 = 0c) x4 + 2x² = 10d) x6 + x³ – 4 = 0e) 2x8 –
Show that x² + 8x + 16 ≥ 0 for all values of x.
a) Factorise 10x² − 29x − 21.b) Hence or otherwise solve the equation 10x² − 29x = 21.
Solve these simultaneous equation.y = x² − 6x + 5y = x − 1
A piece of card has a length of (2x – 1) cm and a width of (x + 2) cm.A square of side xcm is removed from the card. The area of the card thatis left is 68 cm². Find the area of the card that has
Solve each of these inequalities. Sketch the curve for each, showing the interval that satisfies each inequality.a) x² – 2x > 35b) x² + 6 ≤ 5xc) x² ≤ x + 20d) x(x + 3) ≥ 10e) x² <
Write each of these expressions in the form a(x + b)² + c or c - a(x + b)².a) 6x² + 12x – 3b) 3x² – 6x – 15c) 3x² – 18x + 4d) 4x² + 24x – 9e) 5 – 2x – 2x²f) 5x² – 20x + 2g) 4
Use the formula to solve the following inequalities. Leave your answers in surd form.a) 3x² + 10x + 5 < 0 b) x² – 6x + 7 > 0c) 4x² + 3x – 2 > 0d) 2x² + x – 2 ≤ 0 e)
Express each of the quadratic equations in the form y = a (x + b)² + c. Sketch the curve, stating the coordinates of the vertex and whether there is a maximum or minimum value of y. y = 3 −
Use the formula to solve each of these quadratic equations. Write your answers correct to 3 significant figures.a) x4 + 3x² – 5 = 0b) 2x6 – 4x³ + 1 = 0c) 3x6 – 7x3 = 2d) 5x4 + 10x² + 2 = 0e)
Show that 1 + 100x² – 20x ≥ 0 for all values of x.
Solve y6 − 9y³ + 18 = 0.
Solve these simultaneous equation.y = x² − x − 2x + y = 7
Two numbers differ by 4. Their product is 21. Write down a quadratic equation and solve it to find the two numbers.
Solve each of these equations by completing the square. Leave your answers in surd form.a) 3x² + 12x + 2 = 0b) 3x2 + 6х – 5 = 0c) 5x2 + 50x – 7 = 0d) 3 + 20x – 2x² = 0e) 2x² – 8x + 1 = 0
Express each of the quadratic equations in the form y = a (x + b)² + c. Sketch the curve, stating the coordinates of the vertex and whether there is a maximum or minimum value of y.y = x² + 4x − 3
If 2x² – ax + 8 = 0 has no real roots, find the range of possible values of a.
By using the substitution y = √x or otherwise, solve the equation 2x − 5√x + 2 = 0.
Solve these simultaneous equation.y = 2xy = x² − x + 2
Solve 2x² + 5x/x² + 3x + 2 = 4.
Solve each of these inequalities by completing the square. Leave your answers in surd form.a) x² + 4x + 2 < 0b) x² – 6x – 3 ≥ 0 c) x² – 2x – 1 > 0d) x2 + 10x + 7 ≤ 0 e)
Express each of the quadratic equations in the form y = a (x + b)² + c. Sketch the curve, stating the coordinates of the vertex and whether there is a maximum or minimum value of y.y = 5 + 2x − x²
If 6 – 2x – kx² = 0 has a repeated root, find the value of k.
Solve the equation 2x6 − 16x³ − 3 = 0 by completing the square. Write your answer correct to 3 significant figures.
Solve these simultaneous equation.y = x² − 2x − 5y = x + 5
Express each of the quadratic equations in the form y = a (x + b)² + c. Sketch the curve, stating the coordinates of the vertex and whether there is a maximum or minimum value of y. y = 3 + 4x
The equation x² + px + q = 0, where p and q are constants, has roots −3 and 2.Find the value of p and q.
A square piece of card with sides x cm has squares of sides 3 cm cut from the corners. The card is then folded to make an open box with volume 48 cm². Find the dimensions of the card. xcm xcm 3
Solve the equation 3x4 + 5x² = 7 by using the formula. Write your answer correct to 2 decimal places.
Solve these simultaneous equation.y = xy = 6 − x²
Use the discriminant to find the nature of the roots of the equation 3x + 4 = 5/x.
Solve these simultaneous equations.y = 4x + 5y = x
Express each of the quadratic equations in the form y = a (x + b)² + c. Sketch the curve, stating the coordinates of the vertex and whether there is a maximum or minimum value of y.y = x² + 6x + 7
The quadratic equation kx² + 5x + 2 = 0 has two distinct real roots. Find the range of possible values of k.

Showing 700 - 800 of 746

1
2
3
4
5
6
7
8