Daily Practice · Higher Plus
April 2013 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2013, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2013 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2013
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2013y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 2nd April 2013The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 3rd April 2013A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/33. Work out r.
- 4th April 2013On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 5th April 2013Rationalise the denominator of 121/sqrt(11), giving your answer in its simplest form.
- 6th April 2013f(x) = 5x + 9. Work out the inverse function f^-1(x).
- 7th April 2013y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 4.
- 8th April 2013In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 9th April 2013The probability of winning a game is 1/8. A player expects 2 wins. How many games did they play?
- 10th April 2013A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 0.6. How many values in total?
- 11th April 2013Simplify sqrt(18) + sqrt(50), giving your answer in the form a sqrt(b).
- 12th April 2013Solve x^2 + y^2 = 625 and y = x + 17 simultaneously.
- 13th April 2013y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 81.
- 14th April 2013In a vector proof you find that vector PQ = 2a + 2b and vector RS = 10a + 10b. What does this show about PQ and RS?
- 15th April 2013A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.
- 16th April 2013On 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?
- 17th April 2013A rectangle is 25 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 18th April 2013Use the iteration x(n+1) = cube root of (11x(n) + 4) with x(0) = 4. Work out x(1) to 3 decimal places.
- 19th April 2013A train slows steadily from 18 m/s to rest in 8 seconds. Work out its deceleration.
- 20th April 2013A cuboid measures 8 cm by 7 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 21st April 2013A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 22nd April 2013A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
- 23rd April 2013Expand and simplify (2 + sqrt(11))(2 - sqrt(11)).
- 24th April 2013Work out the nth term of the quadratic sequence 2, 1, 2, 5, ...
- 25th April 2013y is inversely proportional to x^2. When x = 2, y = 18. Work out y when x = 3.
- 26th April 2013A cuboid measures 5 cm by 8 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 27th April 2013A bag holds 7 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 28th April 2013On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 29th April 2013A block has mass 450 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 30th April 2013The point (2, -1) lies on y = f(x). Write down its image on y = f(x) + 5.