Choose a course and topic, attempt each question and open its complete worked solution when you are ready.
Solve 3x−2<2x+1 and represent the solution on a number line.
Subtract 2x and add 2.
Write \(R=\{(x,x^3):x\text{ is prime and }x
The primes below 10 are 2, 3, 5 and 7. Cubing each gives 8, 27, 125 and 343.
\(R=\{(2,8),(3,27),(5,125),(7,343)\}\).
Write in interval notation: \(-4<x\le6\), \(-12<x<-10\), \(0\le x<7\), and \(3\le x\le4\).
A strict inequality gives a round bracket; inclusion of an endpoint gives a square bracket.
\((-4,6], (-12,-10), [0,7), [3,4]\).
Give two ways to produce a magnetic field.
A permanent magnet produces a field through aligned magnetic domains. Electric current in a conductor, circular coil or solenoid also produces a field; a current-carrying solenoid with an iron core is an electromagnet.
Use a permanent magnet or pass current through a conductor/coil.
Connect 2 Ω, 3 Ω and 6 Ω resistors to obtain (a) 4 Ω(b) 1 Ω.
(a) Put 3 Ω and 6 Ω in parallel: \(R=2\) Ω; place this in series with the 2 Ω resistor to get 4 Ω.
(b) Put all three in parallel: \[\begin{aligned}\frac{1}{R} &= \frac{1}{2}+\frac{1}{3}+\frac{1}{6}\\&= 1\end{aligned}\], hence \(R=1\) Ω.
(a) 2 Ω + (3 Ω ∥ 6 Ω)(b) 2 Ω ∥ 3 Ω ∥ 6 Ω.
Where should an object be placed before a convex lens to obtain a real image of identical size?
At \(2F_1\), rays form an inverted real image at \(2F_2\) with magnification \(-1\).
At twice the focal length - option (B).
State the functions of human testes.
The seminiferous tubules produce male gametes, sperm. Interstitial cells secrete testosterone, which supports sperm formation, maturation of male reproductive organs and development of secondary sexual characters. Testes lie in the scrotum so sperm production occurs below core body temperature.
Testes produce sperm and secrete testosterone.
Which functions are performed by the brain: thinking, heartbeat regulation, balance, or all three?
The forebrain supports thinking, the medulla regulates heartbeat and the cerebellum maintains balance. Therefore all three are brain functions.
All of the above - option (D).
Explain transport of water and mineral ions through a plant.
Root hairs absorb water by osmosis and mineral ions by active transport. They enter xylem vessels. Evaporation from moist mesophyll and diffusion through stomata create transpiration pull, drawing a continuous water column upward; cohesion between water molecules and adhesion to xylem walls maintain the column. Root pressure assists particularly when transpiration is low.
Use chloromethane, \(\ce{CH3Cl}\), to explain formation of a covalent bond.
Carbon has four valence electrons, each H has one and Cl has seven. Carbon shares one pair with each of three H atoms and one pair with Cl. Carbon thereby reaches an octet, each H a duplet, and chlorine an octet while retaining three lone pairs. The shared electron pairs form three C-H single covalent bonds and one C-Cl single covalent bond.