Daily Practice · Higher Plus
April 1997 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1997 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1997
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1997y is directly proportional to sqrt(x). When x = 9, y = 12. Work out y when x = 25.
- 2nd April 1997In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 3rd April 1997The probability of winning a game is 7/10. A player expects 91 wins. How many games did they play?
- 4th April 1997On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 5th April 1997A car covers 790 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.
- 6th April 1997Simplify (x^2 - 9x + 8)/(x - 8).
- 7th April 1997A train slows steadily from 20 m/s to rest in 5 seconds. Work out its deceleration.
- 8th April 1997In a vector proof you find that vector PQ = 3a - 3b and vector RS = 15a - 15b. What does this show about PQ and RS?
- 9th April 1997A bag holds 8 red and n blue counters. The probability of taking a red is 4/5. Work out n.
- 10th April 1997A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 0.6. How many values in total?
- 11th April 1997Rationalise the denominator of 12/sqrt(3), giving your answer in its simplest form.
- 12th April 1997In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?
- 13th April 1997y is inversely proportional to x^2. When x = 4, y = 100. Work out y when x = 5.
- 14th April 1997A cuboid measures 10 cm by 10 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th April 1997A bag holds 3 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th April 1997On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 17th April 1997Simplify sqrt(18) + sqrt(72), giving your answer in the form a sqrt(b).
- 18th April 1997Make x the subject of 4x + 5 = y(x + 5).
- 19th April 1997y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
- 20th April 1997A cuboid measures 9 cm by 14 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st April 1997A bag holds 7 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd April 1997A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 1.4. How many values in total?
- 23rd April 1997A rectangle is 20 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 24th April 1997Write 5/(x + 5) + 5/(x + 4) as a single fraction.
- 25th April 1997y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 16.
- 26th April 1997The 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.
- 27th April 1997A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 1/55. Work out r.
- 28th April 1997On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 29th April 1997Expand and simplify (5 + sqrt(10))(5 - sqrt(10)).
- 30th April 1997Solve 12x^2 + 7x - 12 = 0.