Daily Practice · Higher Plus
January 1978 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1978 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1978
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1978A bag holds 6 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd January 1978On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 3rd January 1978Expand and simplify (6 + sqrt(11))(6 - sqrt(11)).
- 4th January 1978In an algebraic proof, how would you write a multiple of 5 in terms of an integer n?
- 5th January 1978A train slows steadily from 33 m/s to rest in 4 seconds. Work out its deceleration.
- 6th January 1978The 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.
- 7th January 1978A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 8th January 1978A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 0.6. How many values in total?
- 9th January 1978A block has mass 200 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 10th January 1978Make x the subject of 8x + 4 = y(x + 4).
- 11th January 1978y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
- 12th January 1978In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 13th January 1978The probability of winning a game is 1/4. A player expects 10 wins. How many games did they play?
- 14th January 1978On 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?
- 15th January 1978x = 125 and y = 90, each correct to the nearest whole number. Work out the upper bound of x - y.
- 16th January 1978Write 5/(x + 4) + 4/(x - 3) as a single fraction.
- 17th January 1978y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 18th January 1978In a vector proof you find that vector PQ = 3a - 3b and vector RS = 12a - 12b. What does this show about PQ and RS?
- 19th January 1978A bag holds 8 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 20th January 1978A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 21st January 1978A car covers 900 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 22nd January 1978Solve 8x^2 + 22x + 15 = 0.
- 23rd January 1978y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 81.
- 24th January 1978A cuboid measures 14 cm by 7 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th January 1978A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th January 1978On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 27th January 1978Rationalise the denominator of 42/sqrt(7), giving your answer in its simplest form.
- 28th January 1978f(x) = 5x + 4. Work out the inverse function f^-1(x).
- 29th January 1978A train slows steadily from 34 m/s to rest in 8 seconds. Work out its deceleration.
- 30th January 1978A cuboid measures 6 cm by 4 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 31st January 1978A bag holds 7 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?