Daily Practice · Higher Plus
January 1979 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1979 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1979
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1979The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 2nd January 1979A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 3rd January 1979A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 3. How many values in total?
- 4th January 1979Simplify sqrt(72) + sqrt(72), giving your answer in the form a sqrt(b).
- 5th January 1979f(x) = 4x + 4 and g(x) = 2x + 3. Work out fg(6).
- 6th January 1979y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.
- 7th January 1979In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 8th January 1979The probability of winning a game is 3/8. A player expects 30 wins. How many games did they play?
- 9th January 1979On 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?
- 10th January 1979A rectangle is 20 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th January 1979The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 12th January 1979y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 13th January 1979In a vector proof you find that vector PQ = a - 3b and vector RS = 2a - 6b. What does this show about PQ and RS?
- 14th January 1979A bag holds 7 red and n blue counters. The probability of taking a red is 7/15. Work out n.
- 15th January 1979A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
- 16th January 1979Expand and simplify (6 + sqrt(10))(6 - sqrt(10)).
- 17th January 1979A quadratic sequence starts 11, 19, 31, 47. Work out the second difference, and the coefficient of n^2.
- 18th January 1979y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 81.
- 19th January 1979A cuboid measures 7 cm by 11 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th January 1979A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st January 1979On 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?
- 22nd January 1979A block has mass 730 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd January 1979Solve x^2 + 12x + 32 < 0.
- 24th January 1979A train slows steadily from 29 m/s to rest in 4 seconds. Work out its deceleration.
- 25th January 1979A cuboid measures 4 cm by 4 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th January 1979A bag holds 7 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th January 1979A 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?
- 28th January 1979x = 195 and y = 163, each correct to the nearest whole number. Work out the upper bound of x - y.
- 29th January 1979Write x^2 - 12x - 11 in the form (x + a)^2 + b.
- 30th January 1979y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 31st January 1979The 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.