Daily Practice · Higher Plus
April 2011 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2011, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2011 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2011
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2011A cuboid measures 3 cm by 9 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd April 2011A 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?
- 3rd April 2011On 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?
- 4th April 2011A block has mass 340 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 5th April 2011Make x the subject of 6x + 5 = y(x + 5).
- 6th April 2011A train slows steadily from 25 m/s to rest in 8 seconds. Work out its deceleration.
- 7th April 2011A cuboid measures 5 cm by 5 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th April 2011A bag holds 6 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th April 2011A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
- 10th April 2011x = 141 and y = 68, each correct to the nearest whole number. Work out the upper bound of x - y.
- 11th April 2011Write 4/(x - 4) + 5/(x - 6) as a single fraction.
- 12th April 2011y is inversely proportional to x^2. When x = 4, y = 16. Work out y when x = 2.
- 13th April 2011The 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.
- 14th April 2011A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 15th April 2011On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 16th April 2011A car covers 320 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 17th April 2011Solve 12x^2 - 5x - 3 = 0.
- 18th April 2011y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 19th April 2011In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 20th April 2011The probability of winning a game is 7/8. A player expects 42 wins. How many games did they play?
- 21st April 2011A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 22nd April 2011Rationalise the denominator of 22/sqrt(2), giving your answer in its simplest form.
- 23rd April 2011f(x) = 7x - 6. Work out the inverse function f^-1(x).
- 24th April 2011y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 36.
- 25th April 2011In a vector proof you find that vector PQ = 2a + 4b and vector RS = 10a + 20b. What does this show about PQ and RS?
- 26th April 2011A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 27th April 2011On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 28th April 2011Simplify sqrt(18) + sqrt(2), giving your answer in the form a sqrt(b).
- 29th April 2011Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 30th April 2011A train slows steadily from 23 m/s to rest in 10 seconds. Work out its deceleration.