Daily Practice · Higher Plus
September 1984 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1984 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1984
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1984The 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.
- 2nd September 1984A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 3rd September 1984On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 4th September 1984Expand and simplify (4 + sqrt(5))(4 - sqrt(5)).
- 5th September 1984Work out the coordinates of the turning point of y = x^2 - 10x - 13.
- 6th September 1984y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 7th September 1984In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 8th September 1984The probability of winning a game is 1/2. A player expects 40 wins. How many games did they play?
- 9th September 1984A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 10th September 1984A block has mass 730 g (to the nearest 10 g) and volume 9 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 11th September 1984Simplify (x^2 - 13x + 42)/(x - 7).
- 12th September 1984y is directly proportional to sqrt(x). When x = 25, y = 45. Work out y when x = 16.
- 13th September 1984In a vector proof you find that vector PQ = 3a - 4b and vector RS = 15a - 20b. What does this show about PQ and RS?
- 14th September 1984A bag holds 3 red and n blue counters. The probability of taking a red is 3/10. Work out n.
- 15th September 1984On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 16th September 1984x = 142 and y = 26, each correct to the nearest whole number. Work out the upper bound of x - y.
- 17th September 1984In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?
- 18th September 1984A train slows steadily from 17 m/s to rest in 8 seconds. Work out its deceleration.
- 19th September 1984A cuboid measures 14 cm by 5 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th September 1984A bag holds 3 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st September 1984A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 22nd September 1984A car covers 690 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 23rd September 1984Make x the subject of 7x + 7 = y(x + 7).
- 24th September 1984y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.
- 25th September 1984A cuboid measures 9 cm by 4 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th September 1984A 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?
- 27th September 1984On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 28th September 1984Rationalise the denominator of 77/sqrt(11), giving your answer in its simplest form.
- 29th September 1984Write 5/(x - 3) + 4/(x + 6) as a single fraction.
- 30th September 1984y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 2.