Daily Practice · Higher Plus
April 2006 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2006, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2006 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2006
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2006Write 4/(x - 2) + 4/(x - 5) as a single fraction.
- 2nd April 2006y is directly proportional to sqrt(x). When x = 36, y = 30. Work out y when x = 9.
- 3rd April 2006A cuboid measures 9 cm by 8 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th April 2006A bag holds 3 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th April 2006On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 6th April 2006Simplify sqrt(27) + sqrt(3), giving your answer in the form a sqrt(b).
- 7th April 2006Solve 4x^2 - 16x + 15 = 0.
- 8th April 2006A train slows steadily from 12 m/s to rest in 4 seconds. Work out its deceleration.
- 9th April 2006The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 10th April 2006A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
- 11th April 2006A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 12th April 2006A rectangle is 25 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 13th April 2006f(x) = 6x + 1. Work out the inverse function f^-1(x).
- 14th April 2006y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
- 15th April 2006In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 16th April 2006The probability of winning a game is 7/8. A player expects 42 wins. How many games did they play?
- 17th April 2006On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 18th April 2006Expand and simplify (6 + sqrt(10))(6 - sqrt(10)).
- 19th April 2006Solve x^2 + y^2 = 100 and y = x + 2 simultaneously.
- 20th April 2006y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
- 21st April 2006In a vector proof you find that vector PQ = 6a + b and vector RS = 12a + 2b. What does this show about PQ and RS?
- 22nd April 2006A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 23rd April 2006A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 3. How many values in total?
- 24th April 2006A block has mass 330 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 25th April 2006Use the iteration x(n+1) = cube root of (8x(n) + 7) with x(0) = 3. Work out x(1) to 3 decimal places.
- 26th April 2006y is directly proportional to sqrt(x). When x = 16, y = 8. Work out y when x = 64.
- 27th April 2006A cuboid measures 5 cm by 12 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th April 2006A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th April 2006On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 30th April 2006x = 116 and y = 98, each correct to the nearest whole number. Work out the upper bound of x - y.