Daily Practice · Higher Plus
April 2007 - Higher Plus 5-a-day
Every Higher Plus sheet published in April 2007, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' April 2007 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 2007
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 2007x = 140 and y = 121, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd April 2007A quadratic sequence starts 10, 18, 30, 46. Work out the second difference, and the coefficient of n^2.
- 3rd April 2007A train slows steadily from 35 m/s to rest in 10 seconds. Work out its deceleration.
- 4th April 2007The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 5th April 2007A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 6th April 2007A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 0.8. How many values in total?
- 7th April 2007A car covers 310 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 8th April 2007Solve x^2 + 9x + 20 < 0.
- 9th April 2007y is inversely proportional to x^2. When x = 3, y = 8. Work out y when x = 2.
- 10th April 2007In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 11th April 2007The probability of winning a game is 1/4. A player expects 10 wins. How many games did they play?
- 12th April 2007On 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?
- 13th April 2007Rationalise the denominator of 30/sqrt(6), giving your answer in its simplest form.
- 14th April 2007Write x^2 - 14x - 2 in the form (x + a)^2 + b.
- 15th April 2007y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 2.
- 16th April 2007In a vector proof you find that vector PQ = 2a + b and vector RS = 10a + 5b. What does this show about PQ and RS?
- 17th April 2007A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 18th April 2007A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
- 19th April 2007Simplify sqrt(50) + sqrt(2), giving your answer in the form a sqrt(b).
- 20th April 2007Work out the coordinates of the turning point of y = x^2 - 8x - 13.
- 21st April 2007y is directly proportional to sqrt(x). When x = 25, y = 45. Work out y when x = 81.
- 22nd April 2007A cuboid measures 3 cm by 11 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd April 2007A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th April 2007On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 25th April 2007A rectangle is 11 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th April 2007Simplify (x^2 + 5x - 14)/(x - 2).
- 27th April 2007A train slows steadily from 27 m/s to rest in 10 seconds. Work out its deceleration.
- 28th April 2007A cuboid measures 14 cm by 9 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th April 2007A bag holds 5 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th April 2007A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?