Daily Practice · Higher Plus
January 1984 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1984 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1984
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1984A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 1.4. How many values in total?
- 2nd January 1984A block has mass 280 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 3rd January 1984The point (5, -4) lies on y = f(x). Write down its image on y = -f(x).
- 4th January 1984y is inversely proportional to x^2. When x = 5, y = 48. Work out y when x = 4.
- 5th January 1984The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 6th January 1984A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 7th January 1984On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 8th January 1984x = 76 and y = 36, each correct to the nearest whole number. Work out the upper bound of x - y.
- 9th January 1984Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 10th January 1984y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 11th January 1984In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 12th January 1984The probability of winning a game is 3/5. A player expects 15 wins. How many games did they play?
- 13th January 1984A histogram has two bars: one 5 units wide with frequency density 1.5, one 5 units wide with density 3.5. How many values in total?
- 14th January 1984A car covers 870 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 15th January 1984f(x) = 5x + 3 and g(x) = 3x + 6. Work out fg(0).
- 16th January 1984y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 49.
- 17th January 1984In a vector proof you find that vector PQ = 2a - 6b and vector RS = 6a - 18b. What does this show about PQ and RS?
- 18th January 1984A bag holds 6 red and n blue counters. The probability of taking a red is 6/13. Work out n.
- 19th January 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?
- 20th January 1984Rationalise the denominator of 35/sqrt(7), giving your answer in its simplest form.
- 21st January 1984The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 22nd January 1984A train slows steadily from 17 m/s to rest in 8 seconds. Work out its deceleration.
- 23rd January 1984A cuboid measures 10 cm by 10 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th January 1984A 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?
- 25th January 1984A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 3.5. How many values in total?
- 26th January 1984Simplify sqrt(50) + sqrt(2), giving your answer in the form a sqrt(b).
- 27th January 1984A quadratic sequence starts 0, -1, 0, 3. Work out the second difference, and the coefficient of n^2.
- 28th January 1984y is inversely proportional to x^2. When x = 5, y = 4. Work out y when x = 2.
- 29th January 1984A cuboid measures 10 cm by 13 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th January 1984A bag holds 6 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 31st January 1984On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?