Daily Practice · Higher Plus
January 1974 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1974 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1974
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1974The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 2nd January 1974A train slows steadily from 22 m/s to rest in 5 seconds. Work out its deceleration.
- 3rd January 1974In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 4th January 1974The probability of winning a game is 4/5. A player expects 48 wins. How many games did they play?
- 5th January 1974A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 0.8. How many values in total?
- 6th January 1974x = 140 and y = 125, each correct to the nearest whole number. Work out the upper bound of x - y.
- 7th January 1974A quadratic sequence starts 2, 7, 18, 35. Work out the second difference, and the coefficient of n^2.
- 8th January 1974y is inversely proportional to x^2. When x = 5, y = 72. Work out y when x = 6.
- 9th January 1974In a vector proof you find that vector PQ = 6a + 3b and vector RS = 24a + 12b. What does this show about PQ and RS?
- 10th January 1974A bag holds 7 red and n blue counters. The probability of taking a red is 7/11. Work out n.
- 11th January 1974On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 12th January 1974A car covers 340 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.
- 13th January 1974Solve x^2 - 10x + 16 > 0.
- 14th January 1974y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 15th January 1974A cuboid measures 5 cm by 3 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th January 1974A bag holds 8 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th January 1974A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 3. How many values in total?
- 18th January 1974Rationalise the denominator of 28/sqrt(7), giving your answer in its simplest form.
- 19th January 1974Write x^2 + 8x - 7 in the form (x + a)^2 + b.
- 20th January 1974y is directly proportional to sqrt(x). When x = 36, y = 48. Work out y when x = 64.
- 21st January 1974A cuboid measures 5 cm by 6 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd January 1974A bag holds 4 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd January 1974On 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?
- 24th January 1974Simplify sqrt(75) + sqrt(27), giving your answer in the form a sqrt(b).
- 25th January 1974Work out the coordinates of the turning point of y = x^2 + 16x - 15.
- 26th January 1974A train slows steadily from 14 m/s to rest in 4 seconds. Work out its deceleration.
- 27th January 1974The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 28th January 1974A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/9. Work out r.
- 29th January 1974A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 30th January 1974A rectangle is 11 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 31st January 1974Simplify (x^2 - 9)/(x - 3).