Daily Practice · Higher Plus
April 1995 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1995 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1995
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1995A cuboid measures 11 cm by 9 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd April 1995A bag holds 7 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd April 1995On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 4th April 1995Expand and simplify (5 + sqrt(7))(5 - sqrt(7)).
- 5th April 1995Solve x^2 + 9x + 20 > 0.
- 6th April 1995y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 7th April 1995The 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.
- 8th April 1995A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 9th April 1995A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 10th April 1995A block has mass 890 g (to the nearest 10 g) and volume 17 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 11th April 1995Write x^2 + 6x + 5 in the form (x + a)^2 + b.
- 12th April 1995y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 49.
- 13th April 1995In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 14th April 1995The probability of winning a game is 3/4. A player expects 27 wins. How many games did they play?
- 15th April 1995On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 16th April 1995x = 55 and y = 7, each correct to the nearest whole number. Work out the upper bound of x - y.
- 17th April 1995Work out the coordinates of the turning point of y = x^2 + 4x - 9.
- 18th April 1995A train slows steadily from 30 m/s to rest in 5 seconds. Work out its deceleration.
- 19th April 1995In a vector proof you find that vector PQ = a - 5b and vector RS = 2a - 10b. What does this show about PQ and RS?
- 20th April 1995A bag holds 5 red and n blue counters. The probability of taking a red is 5/7. Work out n.
- 21st April 1995A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 3. How many values in total?
- 22nd April 1995A car covers 120 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.
- 23rd April 1995Simplify (x^2 + 6x + 8)/(x + 4).
- 24th April 1995y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
- 25th April 1995A cuboid measures 14 cm by 12 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th April 1995A bag holds 9 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th April 1995On 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?
- 28th April 1995Rationalise the denominator of 21/sqrt(3), giving your answer in its simplest form.
- 29th April 1995In an algebraic proof, how would you write a multiple of 7 in terms of an integer n?
- 30th April 1995y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.