Daily Practice · Higher Plus
April 2008 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2008, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2008 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2008
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2008Expand and simplify (3 + sqrt(10))(3 - sqrt(10)).
- 2nd April 2008Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.
- 3rd April 2008y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 6.
- 4th April 2008In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 5th April 2008The probability of winning a game is 1/4. A player expects 3 wins. How many games did they play?
- 6th April 2008On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 7th April 2008A block has mass 650 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.
- 8th April 2008Use the iteration x(n+1) = cube root of (4x(n) + 5) with x(0) = 2. Work out x(1) to 3 decimal places.
- 9th April 2008y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 4.
- 10th April 2008In a vector proof you find that vector PQ = 2a - 4b and vector RS = 4a - 8b. What does this show about PQ and RS?
- 11th April 2008A bag holds 3 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 12th April 2008A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 13th April 2008x = 51 and y = 38, each correct to the nearest whole number. Work out the upper bound of x - y.
- 14th April 2008Work out the nth term of the quadratic sequence 13, 27, 47, 73, ...
- 15th April 2008y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 49.
- 16th April 2008A cuboid measures 6 cm by 13 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th April 2008A bag holds 7 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th April 2008On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 19th April 2008A car covers 160 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.
- 20th April 2008The point (-2, 3) lies on y = f(x). Write down its image on y = f(x) + 5.
- 21st April 2008A train slows steadily from 23 m/s to rest in 10 seconds. Work out its deceleration.
- 22nd April 2008A cuboid measures 13 cm by 13 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd April 2008A bag holds 5 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th April 2008A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
- 25th April 2008Rationalise the denominator of 36/sqrt(6), giving your answer in its simplest form.
- 26th April 2008Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 27th April 2008y is inversely proportional to x^2. When x = 3, y = 64. Work out y when x = 4.
- 28th April 2008The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 29th April 2008A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 30th April 2008On 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?