Daily Practice · Higher Plus
April 2012 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2012, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2012 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2012
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2012A cuboid measures 6 cm by 11 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd April 2012A bag holds 3 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd April 2012A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 4th April 2012A rectangle is 24 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 5th April 2012The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 6th April 2012y is inversely proportional to x^2. When x = 2, y = 25. Work out y when x = 5.
- 7th April 2012The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 8th April 2012A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 9th April 2012On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 10th April 2012Expand and simplify (4 + sqrt(2))(4 - sqrt(2)).
- 11th April 2012A quadratic sequence starts 16, 33, 58, 91. Work out the second difference, and the coefficient of n^2.
- 12th April 2012y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 2.
- 13th April 2012In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 14th April 2012The probability of winning a game is 3/10. A player expects 18 wins. How many games did they play?
- 15th April 2012A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
- 16th April 2012A block has mass 540 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 17th April 2012Solve x^2 + 5x > 0.
- 18th April 2012y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 25.
- 19th April 2012In a vector proof you find that vector PQ = 5a + 4b and vector RS = 25a + 20b. What does this show about PQ and RS?
- 20th April 2012A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
- 21st April 2012On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 22nd April 2012x = 77 and y = 18, each correct to the nearest whole number. Work out the upper bound of x - y.
- 23rd April 2012Write x^2 + 12x + 10 in the form (x + a)^2 + b.
- 24th April 2012A train slows steadily from 40 m/s to rest in 4 seconds. Work out its deceleration.
- 25th April 2012A cuboid measures 14 cm by 13 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th April 2012A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th April 2012A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 1.4. How many values in total?
- 28th April 2012A car covers 430 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 29th April 2012Work out the coordinates of the turning point of y = x^2 + 8x + 15.
- 30th April 2012y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.