Daily Practice · Higher Plus
April 2014 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2014, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2014 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2014
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2014Solve x^2 + 6x - 7 > 0.
- 2nd April 2014y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 3rd April 2014In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 4th April 2014The probability of winning a game is 1/2. A player expects 55 wins. How many games did they play?
- 5th April 2014A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?
- 6th April 2014x = 99 and y = 49, each correct to the nearest whole number. Work out the upper bound of x - y.
- 7th April 2014Write x^2 + 10x - 6 in the form (x + a)^2 + b.
- 8th April 2014y is directly proportional to sqrt(x). When x = 36, y = 48. Work out y when x = 9.
- 9th April 2014In a vector proof you find that vector PQ = 2a + 3b and vector RS = 8a + 12b. What does this show about PQ and RS?
- 10th April 2014A bag holds 5 red and n blue counters. The probability of taking a red is 5/11. Work out n.
- 11th April 2014On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 12th April 2014A car covers 600 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 13th April 2014Work out the coordinates of the turning point of y = x^2 + 10x - 7.
- 14th April 2014A train slows steadily from 32 m/s to rest in 5 seconds. Work out its deceleration.
- 15th April 2014A cuboid measures 7 cm by 8 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th April 2014A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th April 2014A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 3.5. How many values in total?
- 18th April 2014Rationalise the denominator of 15/sqrt(5), giving your answer in its simplest form.
- 19th April 2014Simplify (x^2 - x - 56)/(x + 7).
- 20th April 2014y is inversely proportional to x^2. When x = 4, y = 16. Work out y when x = 2.
- 21st April 2014A cuboid measures 5 cm by 9 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd April 2014A bag holds 5 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd April 2014On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 24th April 2014Simplify sqrt(45) + sqrt(45), giving your answer in the form a sqrt(b).
- 25th April 2014In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 26th April 2014y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 5.
- 27th April 2014The 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.
- 28th April 2014A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 36/55. Work out r.
- 29th April 2014A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 30th April 2014A rectangle is 17 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.