Daily Practice · Higher Plus
January 2003 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2003, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2003 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2003
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2003In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 2nd January 2003The probability of winning a game is 1/4. A player expects 13 wins. How many games did they play?
- 3rd January 2003On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4th January 2003A car covers 460 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.
- 5th January 2003Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 6th January 2003y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 7th January 2003In a vector proof you find that vector PQ = 6a + 5b and vector RS = 18a + 15b. What does this show about PQ and RS?
- 8th January 2003A bag holds 5 red and n blue counters. The probability of taking a red is 5/11. Work out n.
- 9th January 2003A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 1.4. How many values in total?
- 10th January 2003Rationalise the denominator of 6/sqrt(3), giving your answer in its simplest form.
- 11th January 2003f(x) = 6x - 1 and g(x) = 2x + 9. Work out fg(1).
- 12th January 2003y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 16.
- 13th January 2003A cuboid measures 10 cm by 11 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th January 2003A 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?
- 15th January 2003On 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?
- 16th January 2003Simplify sqrt(18) + sqrt(32), giving your answer in the form a sqrt(b).
- 17th January 2003The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 18th January 2003A train slows steadily from 12 m/s to rest in 5 seconds. Work out its deceleration.
- 19th January 2003A cuboid measures 8 cm by 10 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th January 2003A bag holds 5 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st January 2003A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 22nd January 2003A rectangle is 23 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 23rd January 2003A quadratic sequence starts 8, 16, 32, 56. Work out the second difference, and the coefficient of n^2.
- 24th January 2003y is inversely proportional to x^2. When x = 5, y = 12. Work out y when x = 2.
- 25th January 2003The 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.
- 26th January 2003A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 27th January 2003On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 28th January 2003Expand and simplify (4 + sqrt(2))(4 - sqrt(2)).
- 29th January 2003Solve x^2 + 4x + 3 > 0.
- 30th January 2003y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 5.
- 31st January 2003In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.